Generally, in a fuel injection system for an internal combustion engine, the fuel supplied from a fuel pump is accumulated in a common-rail (accumulator) and then supplied to each fuel injector. JP-2008-274842A describes that a pressure reducing valve is opened to reduce the fuel pressure in the common-rail when the fuel pressure in the common-rail exceeds a target pressure. When the fuel pressure in the common-rail becomes lower than or equal to the target pressure, the pressure reducing valve is closed.
However, a time lag (response delay time) exists from the time when a command signal is generated to open or close the pressure reducing valve until the time when the pressure reducing valve is actually operated. Thus, it is necessary to control the pressure reducing valve in view of the time lag. However, a method for accurately detecting the response delay time has not been proposed.